Bernardo chooses a three-digit positive integer N and writes both its base- 5 and base- 6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer S. For example, if N=749, Bernardo writes the numbers 10,444 and 3,245, and LeRoy obtains the sum S=13,689. For how many choices of N are the two rightmost digits of S, in order, the same as those of 2 N ?
Answer Choices
A. 5
B. 10
C. 15
D. 20
E. 25